1) The question contains an unknown unit
The number 8908.8 has to be in units of mass: for example, kg or grams.
Here you indicated L.
I am going to work assuming that L is a mass unit. So you can see the way to solve the problem, but you have to verifiy the real unit of the statement and substitute with it.
With that in mind you can find the density of the liquid from:
density = mass / volume
2) Calculate the volume.
The volume of the liquid is the volume of the vessel, because it is filled.
The volume of the vessel is calculated from the formula of volume for a rectantular prism.
Volume of a rectangular prism = area of the base * height = side * side * height
=> Volume = 10 dm * 4 dm * 6 dm = 240 dm^3 = 240 liter
3) Calculate the density:
density = mass /volume = 8,908.8 L / 240 liter = 37.12 L / dm^3
Answer: 37.12 L / dm^3